How do you write an equation in standard form given a line that passes through (-2,2) , perpendicular to y=4?

$x = - 2$
This line $y = 4$ is horizontal. Any line perpendicular to it will be vertical, having a fixed value of $x$, so will be of the form $x = k$ for some constant $k$.
If the line passes through $\left(- 2 , 2\right)$ then that point must satisfy the equation of the line. Hence $k = - 2$.